Very well. Take this one, then.
The General stabbed Dr. Snell with the arrow before high noon began. It didn’t pierce all the way through his heart yet, and the victim did not even notice he had been stabbed due to his back pain medication. The falling glass pane then pushed it in further
The arrow did not pierce or touch Dr. Snell’s skin before high noon! This includes fringe cases of strange contraptions or mechanics that would allow the arrow to take an inordinate amount of time to actually hit him after being set in motion. The arrow both was initially set in motion and pierced his skin at high noon!
Okay, brilliant myster there ghagler. And I probably will not be able to solve this that easily… 
Okay so, by 11.45, the victim was the only one in the room.
Repeat it: When saying everybody who entered the room left by 11.45 with the exception of the victim, all of these people left using the front door!
We know that until 11.45 the keycard was on Dr. Snell, in the living room. May I ask which period of time this holds? Or rather, did Dr. Snell have it on his person the entire day?
There is also the matter of the past. For several months even, this message was visible at high noon precisely. So somebody must have had it everyday.
Or… A much simpler solution. On the day of the murder, the roof access door was never locked!
Thereby evading the need to get/replace the keycard from Dr. Snell.
When saying everybody who entered the room left by 11.45 with the exception of the victim, all of these people left using the front door! I should also clarify, given the next statement:
By this, I meant: Dr. Snell’s keycard remained on his person at all times that day up to and including 11:45; the “within the living room” part was actually meant in context of where he was then (dead, when his body was discovered). It doesn’t mean all day, since he was at the university with his keycard just a few hours earlier. Furthermore: “with the exception of the victim” in the previous Red shouldn’t be taken as a further Red Truth the victim was present in the room at 11:45, but rather a Red that “the victim is not necessarily bound by this Red” and thus could be in the room. Figured that should be cleared up, given the possible misunderstandings I was seeing.
Now, on to the rest:
The roof access door is always locked unless the keycard is swiped, at which point the door remains unlocked until closed, where it will auto-lock. It can be opened from the roof-side even if locked; however, that did not happen at any point on the day of Dr. Snell’s murder, June 19th (henceforth, “June 19” and “the day of Dr. Snell’s murder” refer to the same day).
Repetition requested: The victim’s death was due to a real murder, no suicide or accidental death involved.
Dr. Snell was murdered by the direct action of a separate, distinct human being who knew what they were doing! cacklecackle
Repetition requested: A human being refers to a single consciousness within a single body.
Intriguing mystery. I hope you don’t mind a nobody such as myself taking a crack at it.
Dr. Snell had been observing the strange phenomenon of the mysterious letters formed by light for months. The letters were caused by a glass panel that could only be reliably placed every day by Dr. Snell himself. Thus, it was all a charade set up by Dr. Snell himself. The words spoke of vengeance upon somebody, and General Hartmeyer testified that he spoke of a plan finally coming to fruition and having the bearing of a man finally about to get his revenge. Additionally, his own doctor testified him to be of sound mind. It would be reasonable to conclude Dr. Snell was planning bloody vengeance upon someone. As the charade took the form of Egyptian superstition, it suggests the intended target was professor Wren, who was the only suspect with a connection to the victim related to Egypt and superstition, but that is beside the point.
If Dr. Snell was indeed planning murder, by the arrow inscribed with something related to wrath of Ra, then all restrictions to access to the roof are out of the window for anyone who might have been Snell’s accomplice in this murder, or for Snell’s intended target. Therefore, I propose the following:
Dr. Snell was planning to murder someone, likely professor Wren. The method for this murder would’ve been to set up the arrow pointing upwards under the window in the roof, and dropping his victim onto the arrow. However, Snell himself became the victim, as his intended victim realized what he is up to and defended himself by pushing Snell down through the window. Snell fell onto the arrow, dying instantly. Snell was either pushed through the glass pane, breaking it in the process, or the glass pane was dropped after Snell fell. Afterwards, the killer left the scene through the door, which was unlocked.
Alternatively, Snell had set up an accomplice ready to fire down from the roof with a bow, or drop the arrow should the height be enough for the arrow to gain enough velocity to pierce skin that way. However, something went wrong and Snell ended up under the arrow instead of the intended victim. Perhaps the accomplice betrayed Snell for whatever reason, perhaps Snell struggled with the intended victim and ended up unconscious where the arrow would fall.
I hope I didn’t overlook any reds already stated. It is late night, but the mystery was too interesting to leave untouched.
Alright then, another Repetition if you don’t mind:
The killer acted on their own. There are no accomplices involved. By that I mean none of the suspects involved helped each other commit murder.
Eheheh—of course! In all Red Truth, “human” refers to a single human person with a single human body. We’re sticking with Aristotle here, so no multiple bodies or consciousnesses or any of the like.
An intriguing discussion, @midsummer! But I’m afraid your shots have missed.
Dr. Snell lay dead on his back. Falling onto an arrow would be impossible, and would also not count as “by the direct act of another”, as stated in a previous Red.
Furthermore! An arrow dropped from the roof would not gain the velocity needed to kill Dr. Snell! A bow would be required for a roof-to-living-room shot, and no bow was conveniently lying around on the roof! It would need to be snuck in. Which brings you back to the problem of how to get onto the roof in the first place!
As for dear @Antra: I refuse! cacklecackle I have been generous with my Red in clarifying matters, but don’t expect me to give everything away!
Don’t you worry: I will be sure to strike with plenty of Red. When the time is right.
Very well. It seems the narrative never specifies the camera footage makes it impossible for anyone to have snuck a bow into the roof or out of the roof. Thus, let me adjust my second blue to account for the bow as well.
Dr. Snell let someone onto the roof with a bow. The bow was smuggled in a way that the cameras did not pick up. The bowman stayed on the roof until around 11:50, and shot Snell dead through the window. Afterwards, he left through the door. The door was ajar when the bowman was on the roof, and thus remained unlocked. He took the bow with him and smuggled it away.
Additionally, as this should be information clear to the investigator at the scene, might I ask that you clarify whether the arrow was sticking out of Snell’s body at an angle that suggests Snell was standing when hit if the arrow came from the window, or was it sticking out in an angle that suggests that he was lying on the floor when the arrow hit him?
Dr. Snell did not let anyone onto the roof! Furthermore, (to prevent any zany theories of corridor-shooting) any shot from outside the roof could never make it through the window down into the living room!
Regarding the arrow: The arrow pierced Dr. Snell’s heart as he was standing. Due to the body’s collapse on the floor, the exact angle of the arrow’s penetration is questionable; but it was clear that he fell down, dead.
Alright then, I know this is crazy but it’s the best I got.
The bow and arrow was placed on the roof in a secret spot no one but Snell knew. This was done before the day of the murder.
On the day of the murder, Dr. Snell entered the roof using his key-card. He never closed the roof’s door. Dr. Snell took the bow and arrow out of it’s hiding place and left it out in the open. After that, he got into the living room using the grate and took the key-card with him.
After the killer’s business was done, they entered the roof using the unlocked and open roof door. They discovered the bow and arrow out in the open. The killer got an idea to kill Snell using the bow and arrow. They waited until High Noon, jumped down and stabbed Snell. After that the killer climbed back out of the crate and disposed of the bow by throwing it down the roof. The killer left through the still unlocked roof door.
Good God, I cannot believe I seriously typed that out.
Ahahahaha! Do you think so little of the poor Doctor? Your theory’s almost as fantastic as magic!
Neither bow nor arrow was hidden on the roof or anywhere on the premises. Dr. Snell did not own a bow.
Yeah, that tears it. I need to take a break for today if that pile of crap up there is the best I can come up with after hours of thinking. Ugh
Well done. You managed to corner me to the point that I put out a theory almost as ridiculous as small bombs. I honestly have to give you my respect.
I have high hopes for you! I shall eagerly await your return…
Actually…
After rereading the Prologue, I think I’ve been tackling this mystery all wrong. I’ve been completely focused on making this tale possible by human hands that I completely forgot about the mysteries surrounding the crime. I’m not thinking about why this happened in the first place. Your tale even criticizes Battler for not thinking about what’s going on around him.
“You’re so stupid, Battler,” she said, rubbing her temple. “So incurably imbecilic! It’s like I’m making gameboards for a monkey!”
“Huh?!”
“Do you even bother to think about what’s happening? Why things are happening? Are you just reading the Red and nothing else? Not that it matters—if you had half a brain, you’d be able to actually use the Red for something besides discounting your own theories…”
So instead of banging my head against the wall, I’m gonna at least try to figure out Who did it, and most importantly, Why.
Until then, see you again.
I don’t want to drop the idea that Snell was planning to murder someone but the plan backfired, but as long as I have moves left, I might as well use them even if they don’t line up with that particular theory.
Dr. Snell entered the roof around 11:50. Unbeknownst to him, he was followed to the roof. On the roof, he was stabbed with the arrow. His body fell down through the window.
…Actually, I need not even discard the “Dr. Snell’s revenge plot” -theory. Dr. Snell was planning to murder professor Wren. His plan was to have Wren be down in the living room studying the mysterious letters that would appear at high noon, giving Dr. Snell the perfect shot to shoot him dead with an arrow inscribed with karmic retribution. However, Wren followed Snell to the roof, and stabbed him with the arrow there. Afterwards, he either smuggled the bow out of the building, or perhaps he threw it off the roof far enough and went to retrieve it after he left the building proper.
As for how the murderer could’ve followed Dr. Snell to the roof, perhaps Dr. Snell simply left the door open.
Dr. Snell didn’t own a bow? The bow belonged to someone else. Perhaps Dr. Snell borrowed it for his plan.
I know you said that Dr. Snell was killed by another person but I just want to make sure of something. I’m requesting repetition in red:
Dr. Snell did not want to die.
Repeat it in red! The roof access door was locked on the day of the murder the entire time before high noon!